Revisiting sea-level budget by considering all potential impact factors for global mean sea-level change estimation

Accurate estimates of global sea-level change from the observations of Altimetry, Argo and Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-on (GRACE-FO) are of great value for investigating the global sea-level budget. In this study, we analyzed the global sea-level change over the period from January 2005 to December 2019 by considering all potential impact factors, i.e. three factors for Altimetry observations (two Altimetry products, ocean bottom deformation (OBD) and glacial isostatic adjustment (GIA)), three factors for Argo observations (four Argo products, salinity product error and deep-ocean steric sea-level change), and seven factors for GRACE/GRACE-FO observations including three official RL06 solutions, five spatial filtering methods, three GIA models, two C20 (degree 2 order 0) products, Geocenter motion, GAD field and global mass conservation. The seven impact factors of GRACE/GRACE-FO observations lead to ninety combinations for the post-procession of global mean barystatic sea-level change estimation, whose rates range from 2.00 to 2.45 mm/year. The total uncertainty of global barystatic sea-level change rate is ± 0.27 mm/year at the 95% confidence level, estimated as the standard deviation of the differences between the different datasets constituting the ensembles. The statistical results show that the preferred GIA model developed by Caron et al. in 2018 can improve the closure of the global sea-level budget by 0.20–0.30 mm/year, which is comparable with that of neglecting the halosteric component. About 30.8% of total combinations (GRACE/GRACE-FO plus Argo) can close the global sea-level budget within 1-sigma (0.23 mm/year) of Altimetry observations, 88.9% within 2-sigma. Once the adopted factors including GRACE/GRACE-FO solutions from Center for Space Research (CSR), Caron18 GIA model, SWENSON filtering and Argo product from China Second Institute of Oceanography, the linear trend of global sterodynamic sea-level change derived from GRACE/GRACE-FO plus Argo observations is 3.85 ± 0.14 mm/year, nearly closed to 3.90 ± 0.23 mm/year of Altimetry observations.

Data and processing strategies GRACE and GRACE-FO data. We adopt the RL06 solutions of GRACE/GRACE-FO observations provided by the Center for Space Research (CSR), German Geoforschungszentrum (GFZ) and Jet Propulsion Laboratory (JPL) covering the period from January 2005 to December 2019 with 30 months missing data to estimate (2) GMSLsterodynamic − GMSL OBD = GMSL thermosteric + GMSL thermosteric (deep) + GMSLbarystatic , Table 1. Published estimates of global mean sea-level change rates from Altimetry, Argo, GRACE and GRACE-FO solutions [mm/year]. All the statistical results are part results of these above references. Steric includes thermosteric and halosteric contributions and Thermosteric includes only thermosteric contribution.

Barystatic (GRACE GRACE-FO) Steric (Argo) Note
Chambers et al. 11 2005.1-2014. 12 3.17 ± 0.67 2.11 ± 0.36 0.97 ± 0.15 Steric Dieng et al. 10 2004.1-2015. 12 3.49 ± 0.14 2.24 ± 0.10 1.14 ± 0.09 Steric WCRP Global Sea Level Budget Group. 2 2005.1-2015. 12 3.50 ± 0.20 2.30 ± 0. 19 1.30 ± 0.40 Thermosteric Chen et al. 16 2005.1-2015. 12 3.79 ± 0. 18 2.61 ± 0.14 1.11 ± 0.10 Steric Vishwakarma et al. 9 2005.1-2015. 12  www.nature.com/scientificreports/ global mean barystatic sea-level changes. The spherical harmonics (SH) coefficients of the RL06 solutions are truncated to the degree and order 60 and centered with the mean-field of the study period. Two SLR C 20 coefficients (CSR SLR and GSFC SLR Technical Note 14 ) are used to replace the C 20 coefficients of RL06 solutions of GRACE and GRACE-FO observations 21,25 . Since the RL06 solutions do not contain degree-1 (C 11 , S 11 , C 10 ) coefficients and the longest SLR degree-1 coefficients are just until 2017, only independent estimates of CSR GRACE Technical Note 13 (TN-13) 26  where, ρ 0 is the mean density of seawater (1027 kg/m 3 ), and �ρ is the density change as a function of temperature, salinity and pressure, which can be computed using the United Nations Educational, Scientific and Cultural Organization (UNESCO) standard equations 38 . Since the mean salinity is used in Eq. (3), any salinity effect on steric sea-level change is not considered here and we only focus on the thermosteric contribution. Then the global mean thermosteric sea-level change is computed with four Argo products over global oceans farther than 300 km from the coast between the latitudes from 64.5° S to 64.5° N. For the deep-ocean thermosteric component to the global mean separately, normally taking an estimate of 0.10 mm/year 2,9 , here in this study we adopt 0.12 ± 0.03 mm/year according to the estimated result of Chang et al. 39 .  Table 2. Besides, OBD should be corrected due to the changes in ocean mass load 8 , which are computed using the RL06 solutions following the method of Vishwakarma et al. 9 .
The linear trend of the global mean OBD series is − 0.08 ± 0.01 mm/year over the period from January 2005 to December 2019.
Global thermosteric sea-level change from Argo observations. Four Argo products (IPRC, SIO, CSIO and JAMSTEC) are used to compute the global mean thermosteric sea-level change. Due to the salinity conservation over global oceans, we neglect the halosteric component so as to avoid underestimating the linear trend because of the fast salinity drift error after 2016 17 . Figure 3 shows the global mean thermosteric sea-level changes derived from four Argo products, we can find that Argo-based estimates of IPRC, SIO and CSIO agree well with each other, with slight difference relative to that from JAMSTEC. After deleting 30 missing months same as GRACE/GRACE-FO solutions, the re-estimated global mean thermosteric sea-level change rate is 1.28 ± 0.04 mm/year nearly equal to 1.27 ± 0.04 mm/year as that before deleting missing months, but annual and semi-annual amplitudes are with slight differences (Table 3). Besides, the deep-ocean thermosteric sea-level change (> 2000 m) should be added for Argo observations 9 , whose trend contribution is 0.12 ± 0.03 mm/year 39    www.nature.com/scientificreports/ Global barystatic sea-level change from GRACE/GRACE-FO gravity field solutions. From "Global sterodynamic sea-level change from Altimetry observations" and "Global thermosteric sea-level change from Argo observations" sections, the global mean sterodynamic and thermosteric change series are derived from Altimetry and Argo observations after corresponding impact factors (GIA, OBD, Deep-ocean thermosteric sea-level change) being corrected over the period from January 2005 to December 2019. In this subsection, we will estimate the global mean barystatic sea-level changes using the RL06 solutions of GRACE/GRACE-FO observations. As mentioned in "Introduction" section, the barystatic sea-level change estimates from GRACE/ GRACE-FO RL06 solutions are easily affected by the adopted different post-processing strategies, mainly including three official processing centers (CSR, GFZ, JPL), Geocenter motion (GRACE TN-13), two SLR C 20 coefficients (CSR SLR and GSFC SLR TN-14), SLR C 30 (degree 3 order 0) coefficients (GSFC SLR TN-14), five decorrelation filter methods (P4M6, P4M15, SWENSON (P3M6), DUAN and DDK1), Gaussian smoothing (300 km), signal leakage correction (300 km buffer zone), three GIA models (A13, ICE6G-D and Caron18). These postprocessing strategies will lead to ninety combined solutions of global mean barystatic sea-level change estimates, with which we can investigate the effect of these factors on estimating global mean barystatic sea-level changes and closing the global sea-level budget.
RL06 solutions from three official processing centers. Different processing strategies of GRACE/GRACE-FO solutions will bring certain differences in estimating global mean barystatic sea-level change. Three RL06 solutions from different official processing centers are used to estimate the global mean barystatic sea-level change rate over the period from January 2005 to December 2019 in the open ocean mass farther than 300 km from the coast between the latitudes from 64.5° S to 64.5° N. Figure 4a shows the global mean barystatic sea-level change series and linear trends of three official RL06 solutions computed with the global mean barystatic sea-level changes of ninety combined solutions, in which the largest linear trend differences reach 0.09 mm/year (Table 4).
C 20 coefficients correction. Due to the limited ability of GRACE/GRACE-FO for estimating C 20 coefficients, two different SLR C 20 products (CSR SLR vs GSFC SLR TN14) are adopted to replace the GRACE/GRACE-FO C 20 coefficients over the period from January 2005 to December 2019, the results indicating that two SLR C 20 products have the same effects on global mean barystatic sea-level change rate and slight differences in the amplitudes and phases of annual and semi-annual components, the statistical results are presented in Fig. 4b and Table 4.   (Fig. 4c). However, except for the filtering method of DDK1 (2.15 ± 0.05 mm/year), the differences in the global mean barystatic sea-level change rates are less than 0.02 mm/ year among the other four filtering methods. When no filtering is applied, the global mean barystatic sea-level change rate is 2.32 ± 0.05 mm/year, slightly larger than those of all filtering methods (Table 4).
GIA correction. The GIA signal induces significant trends in GRACE solutions that must be removed, which is a crucial factor for estimating barystatic sea-level change from GRACE/GRACE-FO observations. The only way to correct this signal is to use GIA models. However, different groups have independently developed GIA model solutions based on the Toronto ice history reconstruction, by using different implementations of GIA codes and somehow different Earth models, GIA models significantly differ 2 . We corrected the gravity field effect of GIA-related mass redistributions by using three different GIA modelling results: the model namely A13 by A et al. 29    www.nature.com/scientificreports/ and the mean solution Caron18 by Caron et al. 28 , with the linear trends of − 1.10 mm/year, − 1.00 mm/year and − 1.30 mm/year respectively, which accounts for about 50% of the linear trend of total global mean barystatic sea-level change. It is obvious to find that when the GIA model of Caron et al. 28 is used, the global mean barystatic sea-level change rate is higher (2.38 ± 0.05 mm/year) than the A13 and ICE6G-D models (2.18 ± 0.05 and 2.08 ± 0.05 mm/year), the corresponding results are presented in Fig. 4d and Table 4. Our preferred GIA model is the Caron18, which is based on the ICE-6G deglaciation history 43 , while the model by A et al. 29 is based on its predecessor model, ICE-5G. Besides, the A13 and ICE6G-D models are single GIA models, the Caron18 model arises as a weighted mean from a large ensemble of models, where the glaciation history and the solid-Earth rheology have been varied and validated against independent geodetic data 44 .
Other impact factors. The atmospheric and oceanic masses (i.e., the so-called GAD product) are further needed to be added back but with the GAD mean over the ocean removed following the method of Uebbing et al. 7 . For full global barystatic sea-level change, it leads to very similar estimates with a slight difference (0.03 mm/year) for global mean barystatic sea-level change rates from January 2005 to December 2019 regardless of whether adding the GAD field back or not, however, has a certain effect on the annual and semi-annual amplitudes. There is an important issue that should be addressed is that since the CSR SLR and GSFC TN-14 C 20 and C 30 coefficients are estimated by restoring the GAD back, obviously, the GAD C 20 and C 30 coefficients should be ignored to avoid the problem of "double counting" even though the impact is relatively small. Besides, the global mass conservation correction is also corrected following the method of Chen et al. 16 .
Total uncertainty. In previous subsections of "Global barystatic sea-level change from GRACE/GRACE-FO gravity field solutions" section, we mainly analyze the impact factors (including processing center, C 20 , the filtering method, and the GIA correction) for estimating global mean barystatic sea-level change to determine to which extent the factors can bias GRACE/GRACE-FO estimates and compute an ensemble of ninety combinations for GRACE/GRACE-FO post-processing. The total uncertainties are estimated as the standard deviation of the differences between the different datasets constituting the ensembles 20 . This approach is likely to underestimate the uncertainty as it only considers the variability of a limited number of datasets 17 . Table 4 Figure 5 shows the global mean sterodynamic sea-level change estimation from Altimetry and GRACE/ GRACE-FO plus Argo observations over the period January 2005 to December 2019. The average linear trends are 3.61 ± 0.14 mm/year (Barystatic plus Thermosteric) and 3.90 ± 0.23 mm/year (Altimetry), respectively. From Fig. 5, it is obvious to find that the GRACE data differ around 2017 (shown in pink box of bottom subfigure) and there exist some systematic differences since 2016, mainly due to the problems in the accelerometer instrument leading to the increased errors in GRACE gravity solutions 44 .
Besides, we further present the linear trends of the global sea-level budget from January 2005 to December 2019 for Altimetry, Argo and GRACE/GRACE-FO observations over the sub-ensembles with five main factors (processing center, filtering method, GIA model, C 20 correction and Argo product) in Fig. 6. For the linear trend, about 30.8% of 360 combinations (barystatic plus thermosteric) can close the global sea-level budget within 1-sigma of Altimetry observations if the adopted factors include the Caron18 GIA model and 88.9% within 2-sigma. When the impact factors are CSR (processing center), CSR SLR C 20 , SWENSON (filtering method), Caron18 GIA model and CSIO (Argo), respectively, the largest global mean sterodynamic (barystatic plus thermosteric) sea-level change rate among 360 combinations is 3.85 ± 0.14 mm/year, nearly closed to the 3.90 ± 0.23 of Altimetry observations, which are consistent with the results of Tables 3 and 4.

Conclusions and discussions
There exist many impact factors for investigating the global sea-level budget using the GRACE/GRACE-FO RL06 solutions, Altimetry and Argo observations. It is normally recognized that the sea-level budget can be closed within the uncertainty at a global scale, however, failed to be closed since 2016, seems have a systematic www.nature.com/scientificreports/ difference between the global mean sterodynamic sea-level change obtained by the Altimetry and GRACE/ GRACE-FO plus Argo data 17,45,46 . Through the comparison of comprehensive experiments, we take all potential impact factors (shown in Fig. 1) into account to evaluate their effect on the closure of the global sea-level budget from 2005 to 2019. The new results from Altimetry show substantially larger global mean sterodynamic sealevel change rates than those of GRACE/GRACE-FO plus Argo observations, which are comparable to similar estimates from previous studies (as summarized in Table 1). For global barystatic sea-level change estimation, GIA correction has a more remarkable effect than other impact factors, whereas the preferred Caron18 GIA model can contribute more to improve the closure of the global sea-level budget than the A13 and ICE6G-D models. The ensemble-mean global barystatic sea-level change rate is 2.21 mm/year with a total uncertainty of ± 0.27 mm/year at a 95% confidence level estimated with the different datasets constituting the ensemble of ninety post-processed combined solutions. Due to the fast salinity drift error of some Argo data after 2016, which introduced a negative trend leading to the underestimation of steric sea-level change. The re-assessment global sea-level budget just with the thermosteric sea-level change component can decrease the misclosure ~ 0.30 mm/year. We use four Argo products (IPRC, SIO, CSIO and JAMSTEC) to estimate global thermosteric sea-level change, with a mean linear trend of 1.40 ± 0.05 mm/year after adding the deep-ocean thermosteric contribution of 0.12 ± 0.03 mm/year estimated by Chang et al. 39 . After considering all potential impact factors, the updated results show that the linear trends of 360 combinations of global sterodynamic sea-level change derived from GRACE/GRACE-FO plus Argo range from 3.40 ± 0.28 to 3.85 ± 0.28 mm/year, consistent with 3.90 ± 0.46 mm/year of Altimetry observations at a 95 percent confidence level. Considering that the GRACE-FO mission has been observed about four years, further accumulation of observation data will be better to investigate the remaining misclosure of global sea-level budget among three independent observation systems.  www.nature.com/scientificreports/